This question compares Euler's method using two steps with the same integral using four steps. Consider the initial value problem =3 sin (2²) with y (0) = 3. dy dx In this question enter all numerical approximations accurate to at least 4 decimal places. Note that you should carry out calculations at full accuracy, otherwise you will have rounding errors. (a) Use two steps of Euler's method with h = 0.5 to approximate the value of y(1) (i) Enter the approximate value of y (0.5) Number (ii) Enter the approximate value of y (1) Number = (b) Use four steps of Euler's method with h (i) Enter the approximate value of y (0.25) Number (ii) Enter the approximate value of y (0.5) Number (iii) Enter the approximate value of y (0.75) Number (iv) Enter the approximate value of y(1). Number 0.25 to approximate the value of y(1).
This question compares Euler's method using two steps with the same integral using four steps. Consider the initial value problem =3 sin (2²) with y (0) = 3. dy dx In this question enter all numerical approximations accurate to at least 4 decimal places. Note that you should carry out calculations at full accuracy, otherwise you will have rounding errors. (a) Use two steps of Euler's method with h = 0.5 to approximate the value of y(1) (i) Enter the approximate value of y (0.5) Number (ii) Enter the approximate value of y (1) Number = (b) Use four steps of Euler's method with h (i) Enter the approximate value of y (0.25) Number (ii) Enter the approximate value of y (0.5) Number (iii) Enter the approximate value of y (0.75) Number (iv) Enter the approximate value of y(1). Number 0.25 to approximate the value of y(1).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:This question compares Euler's method using two steps with the same integral using four steps.
Consider the initial value problem =3 sin (2²) with y (0) = 3.
dy
dx
In this question enter all numerical approximations accurate to at least 4 decimal places. Note that you should carry out calculations at full accuracy,
otherwise you will have rounding errors.
(a) Use two steps of Euler's method with h = 0.5 to approximate the value of y(1)
(i) Enter the approximate value of y (0.5)
Number
(ii) Enter the approximate value of y (1)
Number
=
(b) Use four steps of Euler's method with h
(i) Enter the approximate value of y (0.25)
Number
(ii) Enter the approximate value of y (0.5)
Number
(iii) Enter the approximate value of y (0.75)
Number
(iv) Enter the approximate value of y (1).
Number
0.25 to approximate the value of y(1).
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